R Workflow

Author

Frank Harrell

Published

May 3, 2022

This article outlines analysis project workflow that I’ve found to be efficient in making reproducible research reports using R with Rmarkdown and now Quarto. I start by covering the creation of annotated analysis files and running descriptive statistics on them with goals of understanding the data and the quality and completeness of the data. Functions in the Hmisc package are used to annotate data frames and data tables with labels and units of measurement and to produce tabular and graphical statistical summaries. Several examples of processing and manipulating data using the data.table package are given. Finally, examples of caching results and doing parallel processing are presented.

Comments

File Directory Structure

I have a directory for each major project, and put everything in that directory (including data files) except for graphics files for figures, which are placed in their own subdirectory underneath the project folder. The directory name for the project includes key identifying information, and files within that directory do not contain project information in their names, nor do they contain dates, unless I want to freeze an old version of an analysis script.

With Quarto I specify that html files are to be self-contained, so there are no separate graphics files.

For multi-analyst projects or ones in which you want to capture the entire code history, having the project on github is worthwhile.

Analysis File Creation

I typically create a compact analysis file in a separate R script called create.r and have it produce compressed R binary data.frame or data.table .rds files using saveRDS(name, 'name.rds', compress='xz'). Then I have an analysis script named for example a.qmd (for Quarto reports) or a.Rmd (for RMarkdown reports) that starts with d <- readRDS('name.rds').

Templates for analysis reports are here, and a comprehensive report example may be found here.

When variables need to be recoded, have labels added or changed, or have units of measurement added, I specify those using the Hmisc package upData function. Here is an example:

Variable labels and units of measurement are used in special ways in my R packages. This will show up in the describe and contents function outputs below and in axis labels for graphics.

# Function to recode from atypical coding for yes/no in raw data
yn <- function(x) factor(x, 0:1, c('yes', 'no'))
d <-
  upData(d,
         rename = c(gender='sex', any.event='anyEvent'),
         posSE    = yn(posSE),
         newMI    = yn(newMI),
         newPTCA  = yn(newPTCA),
         newCABG  = yn(newCABG),
         death    = yn(death),
         hxofHT   = yn(hxofHT),
         hxofDM   = yn(hxofDM),
         hxofCig  = factor(hxofCig, c(0, 0.5, 1),
                           c('heavy', 'moderate', 'non-smoker')), 
         hxofMI   = yn(hxofMI),
         hxofPTCA = yn(hxofPTCA),
         hxofCABG = yn(hxofCABG),
         chestpain= yn(chestpain),
         anyEvent = yn(anyEvent),
         drop=Cs(event.no,phat,mics,deltaEF,  # Cs in Hmisc; auto quotes
           newpkmphr,gdpkmphr,gdmaxmphr,gddpeakdp,gdmaxdp,
           hardness),
         labels=c(
           bhr    ='Basal heart rate',
           basebp ='Basal blood pressure',
           basedp ='Basal Double Product bhr*basebp',
           age    ='Age',
           pkhr   ='Peak heart rate',
           sbp    ='Systolic blood pressure',
           dp     ='Double product pkhr*sbp',
           dose   ='Dose of dobutamine given',
           maxhr  ='Maximum heart rate',
           pctMphr='Percent maximum predicted heart rate achieved',
           mbp    ='Maximum blood pressure',
           dpmaxdo='Double product on max dobutamine dose',
           dobdose='Dobutamine dose at max double product',
           baseEF ='Baseline cardiac ejection fraction',
           dobEF  ='Ejection fraction on dobutamine', 
           chestpain='Chest pain', 
           ecg     ='Baseline electrocardiogram diagnosis',
           restwma ='Resting wall motion abnormality on echocardiogram', 
           posSE   ='Positive stress echocardiogram',
           newMI   ='New myocardial infarction',
           newPTCA ='Recent angioplasty',
           newCABG ='Recent bypass surgery', 
           hxofHT  ='History of hypertension', 
           hxofDM  ='History of diabetes',
           hxofMI  ='History of myocardial infarction',
           hxofCig ='History of smoking',
           hxofPTCA='History of angioplasty',
           hxofCABG='History of coronary artery bypass surgery',
           anyEvent='Death, newMI, newPTCA, or newCABG'),
         units=c(age='years', bhr='bpm', basebp='mmHg', basedp='bpm*mmHg',
           pkhr='mmHg', sbp='mmHg', dp='bpm*mmHg', maxhr='bpm',
           mbp='mmHg', dpmaxdo='bpm*mmHg', baseEF='%', dobEF='%',
           pctMphr='%', dose='mg', dobdose='mg')
         )

saveRDS(d, 'stressEcho.rds', compress='xz')

# Note that we could have automatically recoded all 0:1 variables
# if they were all to be treated identically:

for(x in names(d)) 
  if(all(d[[x]] %in% c(0,1))) d[[x]] <- yn(d[[x]])

If reading data exported from REDCap that are placed into the project directory I run the following to get rid of duplicate (factor and non-factor versions of variables REDCap produces) variables and automatically convert dates to Date variables:

require(Hmisc)
getRs('importREDCap.r', put='source')  # source() code to define function
mydata <- importREDCap()  # by default operates on last downloaded export
saveRDS(mydata, 'mydata.rds', compress='xz')

When file names are not given to importREDCap the function looks for the latest created .csv file and .R file with same prefix and uses those. See this for more information.

Data Dictionary

The Hmisc package contents function will provide a concise data dictionary. Here is an example using the permanent version of the dataset created above, which can be accessed with the Hmisc getHdata function. The top of the contents output has the number of levels for factor variables hyperlinked. Click on the number to go directly to the list of levels for that variable.

The permanent version of stressEcho coded binary variables as 0/1 instead of N/Y.

require(Hmisc)
getHdata(stressEcho)
d <- stressEcho
html(contents(d), levelType='table')

Data frame:d

558 observations and 31 variables, maximum # NAs:0

Name	Labels	Units	Levels	Storage
bhr	Basal heart rate	bpm		integer
basebp	Basal blood pressure	mmHg		integer
basedp	Basal Double Product bhr*basebp	bpm*mmHg		integer
pkhr	Peak heart rate	mmHg		integer
sbp	Systolic blood pressure	mmHg		integer
dp	Double product pkhr*sbp	bpm*mmHg		integer
dose	Dose of dobutamine given	mg		integer
maxhr	Maximum heart rate	bpm		integer
pctMphr	Percent maximum predicted heart rate achieved	%		integer
mbp	Maximum blood pressure	mmHg		integer
dpmaxdo	Double product on max dobutamine dose	bpm*mmHg		integer
dobdose	Dobutamine dose at max double product	mg		integer
age	Age	years		integer
gender			2	integer
baseEF	Baseline cardiac ejection fraction	%		integer
dobEF	Ejection fraction on dobutamine	%		integer
chestpain	Chest pain			integer
restwma	Resting wall motion abnormality on echocardiogram			integer
posSE	Positive stress echocardiogram			integer
newMI	New myocardial infarction			integer
newPTCA	Recent angioplasty			integer
newCABG	Recent bypass surgery			integer
death				integer
hxofHT	History of hypertension			integer
hxofDM	History of diabetes			integer
hxofCig	History of smoking		3	integer
hxofMI	History of myocardial infarction			integer
hxofPTCA	History of angioplasty			integer
hxofCABG	History of coronary artery bypass surgery			integer
any.event	Death, newMI, newPTCA, or newCABG			integer
ecg	Baseline electrocardiogram diagnosis		3	integer

Variable	Levels
gender	male
	female
hxofCig	heavy
	moderate
	non-smoker
ecg	normal
	equivocal
	MI

Descriptive Statistics

The Hmisc describe function is my main tool for getting initial descriptive statistics and quality controlling the data in a univariate fashion. Here is an example. The Info index is a measure of the information content in a numeric variable relative to the information in a continuous numeric variable with no ties. A very low value of Info will occur when a highly imbalanced variable is binary.

Info comes from the approximate formula for the variance of a log odds ratio for a proportional odds model/Wilcoxon test, due to Whitehead.

Gmd stands for Gini’s mean difference—the mean absolute difference over all possible pairs of different observations. It is a very interpretable measure of dispersion that is more robust than the standard deviation.

w <- describe(d)
html(w, scroll=TRUE, rows=50)

d

31 Variables 558 Observations

bhr: Basal heart rate bpm

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	69	0.999	75.29	16.57	54.0	58.0	64.0	74.0	84.0	95.3	102.0

lowest : 42 44 45 46 47 , highest: 108 115 116 127 210

basebp: Basal blood pressure mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	94	0.998	135.3	23.35	104.0	110.0	120.0	133.0	150.0	162.3	170.1

lowest : 85 88 90 97 98 , highest: 192 194 195 201 203

basedp: Basal Double Product bhr*basebp bpm*mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	441	1	10181	2813	6607	7200	8400	9792	11663	13610	14770

lowest : 5000 5220 5280 5400 5460 , highest: 17604 17710 17748 21082 27300

pkhr: Peak heart rate mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	105	1	120.6	25.36	81.85	90.70	106.25	122.00	135.00	147.00	155.15

lowest : 52 61 62 63 66 , highest: 170 171 176 182 210

sbp: Systolic blood pressure mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	142	1	146.9	40.72	96	102	120	141	170	200	210

lowest : 40 60 70 79 80 , highest: 240 250 274 283 309

dp: Double product pkhr*sbp bpm*mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	508	1	17634	5765	10256	11341	14033	17060	20644	24536	26637

lowest : 5100 5940 7490 8100 8360 , highest: 32518 33400 33840 38205 45114

dose: Dose of dobutamine given mg

n	missing	distinct	Info	Mean	Gmd
558	0	7	0.84	33.75	8.334

lowest : 10 15 20 25 30 , highest: 20 25 30 35 40

 Value         10    15    20    25    30    35    40
 Frequency      2    28    47    56    64    61   300
 Proportion 0.004 0.050 0.084 0.100 0.115 0.109 0.538

maxhr: Maximum heart rate bpm

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	103	1	119.4	24.64	82.0	91.0	104.2	120.0	133.0	146.0	154.1

lowest : 58 62 63 66 67 , highest: 170 171 176 182 200

pctMphr: Percent maximum predicted heart rate achieved %

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	78	0.999	78.57	16.86	53	60	69	78	88	97	104

lowest : 38 39 40 41 42 , highest: 116 117 126 132 133

mbp: Maximum blood pressure mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	132	0.999	156	35.03	110.0	120.0	133.2	150.0	175.8	200.0	211.1

lowest : 84 90 92 93 96 , highest: 240 250 274 283 309

dpmaxdo: Double product on max dobutamine dose bpm*mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	484	1	18550	5385	11346	12865	15260	18118	21239	24893	27477

lowest : 7130 8100 8360 9240 9280 , highest: 32518 33400 33840 38205 45114

dobdose: Dobutamine dose at max double product mg

n	missing	distinct	Info	Mean	Gmd
558	0	8	0.941	30.24	10.55

lowest : 5 10 15 20 25 , highest: 20 25 30 35 40

 Value          5    10    15    20    25    30    35    40
 Frequency      7     7    55    73    71    78    62   205
 Proportion 0.013 0.013 0.099 0.131 0.127 0.140 0.111 0.367

age: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	62	0.999	67.34	13.41	46.85	51.00	60.00	69.00	75.00	82.00	85.00

lowest : 26 28 29 30 33 , highest: 89 90 91 92 93

gender

n	missing	distinct
558	0	2

 Value        male female
 Frequency     220    338
 Proportion  0.394  0.606

baseEF: Baseline cardiac ejection fraction %

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	54	0.994	55.6	10.71	32	40	52	57	62	65	66

lowest : 20 21 22 23 25 , highest: 74 75 77 79 83

dobEF: Ejection fraction on dobutamine %

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	60	0.992	65.24	12.38	40.0	49.7	62.0	67.0	73.0	76.0	80.0

lowest : 23 25 26 27 28 , highest: 86 87 89 90 94

chestpain: Chest pain

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.64	172	0.3082	0.4272

restwma: Resting wall motion abnormality on echocardiogram

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.745	257	0.4606	0.4978

posSE: Positive stress echocardiogram

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.553	136	0.2437	0.3693

newMI: New myocardial infarction

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.143	28	0.05018	0.09549

newPTCA: Recent angioplasty

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.138	27	0.04839	0.09226

newCABG: Recent bypass surgery

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.167	33	0.05914	0.1115

death

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.123	24	0.04301	0.08247

hxofHT: History of hypertension

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.625	393	0.7043	0.4173

hxofDM: History of diabetes

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.699	206	0.3692	0.4666

hxofCig: History of smoking

n	missing	distinct
558	0	3

 Value           heavy   moderate non-smoker
 Frequency         122        138        298
 Proportion      0.219      0.247      0.534

hxofMI: History of myocardial infarction

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.599	154	0.276	0.4004

hxofPTCA: History of angioplasty

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.204	41	0.07348	0.1364

hxofCABG: History of coronary artery bypass surgery

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.399	88	0.1577	0.2661

any.event: Death, newMI, newPTCA, or newCABG

n	missing	distinct	Info	Sum	Mean	Gmd
558	0	2	0.402	89	0.1595	0.2686

ecg: Baseline electrocardiogram diagnosis

n	missing	distinct
558	0	3

 Value         normal equivocal        MI
 Frequency        311       176        71
 Proportion     0.557     0.315     0.127

There is also a plot method for describe output. It produces two graphics objects: one for categorical variables and one for continuous variables. The default is to use ggplot2 to produce static graphics.

p <- plot(w)
p$Categorical

p$Continuous

By specifying grType option you can instead get plotly graphics that use hover text to show more information, especially when hovering over the leftmost dot or tick mark for a variable.

options(grType='plotly')
p <- plot(w)
p$Categorical

p$Continuous

See this for other Hmisc functions for descriptive graphics and tables, especially for stratified descriptive statistics for categorical variables. The summaryM function prints a tabular summary of a mix of continuous and categorical variables. Here is an example where stratification is by history of myocardial infarction (MI).

require(data.table)
setDT(d)   # turn d into a data table
w <- d
w[, hxofMI := factor(hxofMI, 0 : 1, c('No history of MI', 'History of MI'))]
vars <- setdiff(names(d), 'hxofMI')
form <- as.formula(paste(paste(vars, collapse='+'), '~ hxofMI'))
print(form)

bhr + basebp + basedp + pkhr + sbp + dp + dose + maxhr + pctMphr + mbp + dpmaxdo + dobdose + age + gender + baseEF + dobEF + chestpain + restwma + posSE + newMI + newPTCA + newCABG + death + hxofHT + hxofDM + hxofCig + hxofPTCA + hxofCABG + any.event + ecg ~ hxofMI

s <- summaryM(form, data=d, test=TRUE)
html(s, exclude1=TRUE, npct='both', digits=3, middle.bold=TRUE)

	No history of MI N=404	History of MI N=154	Test Statistic
Descriptive Statistics (N=558).
Basal heart rate bpm	65 74 85	63 72 84	F_1 556=1.41, P=0.235¹
Basal blood pressure mmHg	120 134 150	120 130 150	F_1 556=1.39, P=0.238¹
Basal Double Product bhrbasebp bpmmmHg	8514 9874 11766	8026 9548 11297	F_1 556=3.32, P=0.069¹
Peak heart rate mmHg	107 123 136	104 120 132	F_1 556=2.35, P=0.126¹
Systolic blood pressure mmHg	124 146 174	115 134 158	F_1 556=12.1, P<0.001¹
Double product pkhrsbp bpmmmHg	14520 17783 21116	13198 15539 18885	F_1 556=15, P<0.001¹
Dose of dobutamine given mg : 10	0.00 ²⁄₄₀₄	0.00 ⁰⁄₁₅₄	χ²₆=8.77, P=0.187²
15	0.05 ²¹⁄₄₀₄	0.05 ⁷⁄₁₅₄
20	0.10 ⁴⁰⁄₄₀₄	0.05 ⁷⁄₁₅₄
25	0.11 ⁴⁵⁄₄₀₄	0.07 ¹¹⁄₁₅₄
30	0.11 ⁴³⁄₄₀₄	0.14 ²¹⁄₁₅₄
35	0.11 ⁴⁵⁄₄₀₄	0.10 ¹⁶⁄₁₅₄
40	0.51 ²⁰⁸⁄₄₀₄	0.60 ⁹²⁄₁₅₄
Maximum heart rate bpm	107 122 134	102 118 130	F_1 556=4.05, P=0.045¹
Percent maximum predicted heart rate achieved %	69.0 78.0 89.0	70.0 77.0 87.5	F_1 556=0.5, P=0.479¹
Maximum blood pressure mmHg	138 154 180	130 142 162	F_1 556=13, P<0.001¹
Double product on max dobutamine dose bpm*mmHg	15654 18666 21664	14489 16785 19680	F_1 556=16.1, P<0.001¹
Dobutamine dose at max double product mg : 5	0.01 ⁴⁄₄₀₄	0.02 ³⁄₁₅₄	χ²₇=8.5, P=0.29²
10	0.01 ⁶⁄₄₀₄	0.01 ¹⁄₁₅₄
15	0.11 ⁴³⁄₄₀₄	0.08 ¹²⁄₁₅₄
20	0.14 ⁵⁸⁄₄₀₄	0.10 ¹⁵⁄₁₅₄
25	0.13 ⁵⁴⁄₄₀₄	0.11 ¹⁷⁄₁₅₄
30	0.13 ⁵¹⁄₄₀₄	0.18 ²⁷⁄₁₅₄
35	0.10 ⁴⁰⁄₄₀₄	0.14 ²²⁄₁₅₄
40	0.37 ¹⁴⁸⁄₄₀₄	0.37 ⁵⁷⁄₁₅₄
Age years	59.0 68.0 75.0	63.2 71.0 76.8	F_1 556=9.75, P=0.002¹
gender : female	0.68 ²⁷³⁄₄₀₄	0.42 ⁶⁵⁄₁₅₄	χ²₁=30, P<0.001²
Baseline cardiac ejection fraction %	55 59 63	40 54 60	F_1 556=56.4, P<0.001¹
Ejection fraction on dobutamine %	65.0 70.0 74.2	50.0 64.5 70.0	F_1 556=50.3, P<0.001¹
Chest pain	0.29 ¹¹⁹⁄₄₀₄	0.34 ⁵³⁄₁₅₄	χ²₁=1.29, P=0.257²
Resting wall motion abnormality on echocardiogram	0.57 ²³⁰⁄₄₀₄	0.18 ²⁷⁄₁₅₄	χ²₁=69.7, P<0.001²
Positive stress echocardiogram	0.21 ⁸⁶⁄₄₀₄	0.32 ⁵⁰⁄₁₅₄	χ²₁=7.56, P=0.006²
New myocardial infarction	0.03 ¹⁴⁄₄₀₄	0.09 ¹⁴⁄₁₅₄	χ²₁=7.4, P=0.007²
Recent angioplasty	0.02 ¹⁰⁄₄₀₄	0.11 ¹⁷⁄₁₅₄	χ²₁=17.8, P<0.001²
Recent bypass surgery	0.05 ²¹⁄₄₀₄	0.08 ¹²⁄₁₅₄	χ²₁=1.35, P=0.246²
death	0.04 ¹⁵⁄₄₀₄	0.06 ⁹⁄₁₅₄	χ²₁=1.23, P=0.267²
History of hypertension	0.69 ²⁸⁰⁄₄₀₄	0.73 ¹¹³⁄₁₅₄	χ²₁=0.89, P=0.346²
History of diabetes	0.36 ¹⁴⁷⁄₄₀₄	0.38 ⁵⁹⁄₁₅₄	χ²₁=0.18, P=0.674²
History of smoking : heavy	0.21 ⁸³⁄₄₀₄	0.25 ³⁹⁄₁₅₄	χ²₂=3.16, P=0.206²
moderate	0.24 ⁹⁶⁄₄₀₄	0.27 ⁴²⁄₁₅₄
non-smoker	0.56 ²²⁵⁄₄₀₄	0.47 ⁷³⁄₁₅₄
History of angioplasty	0.04 ¹⁵⁄₄₀₄	0.17 ²⁶⁄₁₅₄	χ²₁=28.4, P<0.001²
History of coronary artery bypass surgery	0.08 ³⁴⁄₄₀₄	0.35 ⁵⁴⁄₁₅₄	χ²₁=59.6, P<0.001²
Death, newMI, newPTCA, or newCABG	0.12 ⁴⁸⁄₄₀₄	0.27 ⁴¹⁄₁₅₄	χ²₁=18.1, P<0.001²
Baseline electrocardiogram diagnosis : normal	0.59 ²⁴⁰⁄₄₀₄	0.46 ⁷¹⁄₁₅₄	χ²₂=8, P=0.018²
equivocal	0.29 ¹¹⁷⁄₄₀₄	0.38 ⁵⁹⁄₁₅₄
MI	0.12 ⁴⁷⁄₄₀₄	0.16 ²⁴⁄₁₅₄
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. Tests used: ¹Wilcoxon test; ²Pearson test .

plot(s, which='categorical', vars=1 : 4)   # plot first 4 categorical variables

plot(s, which='continuous',  vars=1 : 4)   # plot first 4 continuous variables

Semi-interactive stratified spike histograms are also useful descriptive plots. These plots also contain a superset of the quantiles used in box plots, and the legend is clickable, allowing any of the statistical summaries to be turned off.

d[, histboxp(x=maxhr, group=ecg, bins=200)]

Data Manipulation and Aggregation

The data.table package provides a concise, consistent syntax for managing simple and complex data manipulation tasks, and it is extremely efficient for large datasets. One of the best organized tutorials is this, and a master cheatsheet for data.table is here from which the general syntax below is taken, where DT represents a data table.

   DT[ i,  j,  by ] # + extra arguments
        |   |   |
        |   |    -------> grouped by what?
        |    -------> what to do?
         ---> on which rows?

Data tables are also data frames so work on any method handling data frames. But data tables do not contain rownames.

Several data.table examples follow. I like to hold the current dataset in d to save typing. To facilitate some operations requiring variable names to be quoted, define a function .q to quote them automatically (like the Hmisc function Cs).

.q <- function(...) as.character(sys.call())[-1]
.q(a,b,c)

[1] "a" "b" "c"

Analyzing Selected Variables and Subsets

d[, html(describe(age))]

age: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	62	0.999	67.34	13.41	46.85	51.00	60.00	69.00	75.00	82.00	85.00

lowest : 26 28 29 30 33 , highest: 89 90 91 92 93

d[, html(describe(~ age + gender))]

age + gender

2 Variables 558 Observations

age: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	62	0.999	67.34	13.41	46.85	51.00	60.00	69.00	75.00	82.00	85.00

lowest : 26 28 29 30 33 , highest: 89 90 91 92 93

gender

n	missing	distinct
558	0	2

 Value        male female
 Frequency     220    338
 Proportion  0.394  0.606

d[gender == 'female', html(describe(age))]   # analyze age for females

age: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
338	0	58	0.999	67.01	13.74	47.00	50.70	59.25	68.00	76.00	83.00	85.00

lowest : 26 28 29 33 34 , highest: 87 88 89 90 91

html(describe(d[, .(age, gender)], 'Age and Gender Stats'))

Age and Gender Stats

2 Variables 558 Observations

age: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
558	0	62	0.999	67.34	13.41	46.85	51.00	60.00	69.00	75.00	82.00	85.00

lowest : 26 28 29 30 33 , highest: 89 90 91 92 93

gender

n	missing	distinct
558	0	2

 Value        male female
 Frequency     220    338
 Proportion  0.394  0.606

# Separate analysis by female, male.  Use keyby instead of by to sort the usual way.
d[, print(describe(age, descript=gender)), by=gender]

male : Age [years] 
       n  missing distinct     Info     Mean      Gmd      .05      .10 
     220        0       51    0.999    67.86    12.91    45.95    51.00 
     .25      .50      .75      .90      .95 
   62.00    69.00    75.00    81.00    86.00 

lowest : 30 34 38 40 43, highest: 88 89 91 92 93
female : Age [years] 
       n  missing distinct     Info     Mean      Gmd      .05      .10 
     338        0       58    0.999    67.01    13.74    47.00    50.70 
     .25      .50      .75      .90      .95 
   59.25    68.00    76.00    83.00    85.00 

lowest : 26 28 29 33 34, highest: 87 88 89 90 91

Empty data.table (0 rows and 1 cols): gender

# Compute mean and median age by gender
d[, .(Mean=mean(age), Median=median(age)), by=gender]

   gender     Mean Median
1:   male 67.85909     69
2: female 67.00888     68

# To create a new subset
w <- d[gender == 'female' & age < 70, ]

Adding or Changing Variables

With data.table you can create a new data table with added variables, or you can add or redefine variables in a data table in place. The latter has major speed and memory efficiency implications when processing massive data tables. Here d refers to a different data table from the one used above.

# Rename a variable
setnames(d, c('gender', 'height'), c('sex', 'ht'))
# Easier:
setnames(d, .q(gender, height), .q(sex, ht))

# Add two new variables, storing result in a new data table
z <- d[, .(bmi=wt / ht ^ 2, bsa=0.016667 * sqrt(wt * ht))]

# Add one new variable in place
d[, bmi := wt / ht ^ 2]

# Add two new variables in place
d[, `:=`(bmi = wt / ht ^ 2, bas=0.016667 * sqrt(wt * ht))]
d[, .q(bmi, bsa) := .(wt / ht ^ 2, 0.016667 * sqrt(wt * ht))]

# Add label & optional units (better to use upData which works on data tables)
adlab <- function(x, lab, un='') {
  label(x) <- lab
  if(un != '') units(x) <- un
  x
}
d[, maxhr := adlab(maxhr, 'Maximum Heart Rate', '/m')]

# Delete a variable (or use upData)
d[, bsa := NULL]

# Delete two variables
d[, `:=`(bsa=NULL, bmi=NULL)]
d[, .q(bsa, bmi) := NULL]

Computing Summary Statistics

Many applications can use the automatically created data.table object .SD which stands for the data table for the current group being processed. If .SDcols were not specified, all variables would be attempted to be analyzed. Specify a vector of variable names as .SDcols to restrict the analysis. If there were no by variable(s), .SD stands for the whole data table.

# Compute the number of distinct values for all variables
nd <- function(x) length(unique(x))
d[, sapply(.SD, nd)]

      bhr    basebp    basedp      pkhr       sbp        dp      dose     maxhr 
       69        94       441       105       142       508         7       103 
  pctMphr       mbp   dpmaxdo   dobdose       age    gender    baseEF     dobEF 
       78       132       484         8        62         2        54        60 
chestpain   restwma     posSE     newMI   newPTCA   newCABG     death    hxofHT 
        2         2         2         2         2         2         2         2 
   hxofDM   hxofCig    hxofMI  hxofPTCA  hxofCABG any.event       ecg 
        2         3         2         2         2         2         3

# Same but only for variables whose names contain hx and either D or M
d[, sapply(.SD, nd), .SDcols=patterns('hx', 'D|M')]

hxofDM hxofMI 
     2      2

# Compute means on all numeric variables
mn <- function(x) mean(x, na.rm=TRUE)
d[, lapply(.SD, mn), .SDcols=is.numeric]

        bhr   basebp   basedp     pkhr      sbp       dp     dose    maxhr
1: 75.29032 135.3244 10181.31 120.5502 146.9158 17633.84 33.75448 119.3692
    pctMphr mbp  dpmaxdo  dobdose      age   baseEF    dobEF chestpain
1: 78.56989 156 18549.88 30.24194 67.34409 55.60394 65.24194 0.3082437
     restwma     posSE      newMI   newPTCA    newCABG      death    hxofHT
1: 0.4605735 0.2437276 0.05017921 0.0483871 0.05913978 0.04301075 0.7043011
      hxofDM  hxofPTCA  hxofCABG any.event
1: 0.3691756 0.0734767 0.1577061 0.1594982

# Compute means on all numeric non-binary variables
nnb <- function(x) is.numeric(x) && length(unique(x)) > 2
d[, lapply(.SD, mn), .SDcols=nnb]

        bhr   basebp   basedp     pkhr      sbp       dp     dose    maxhr
1: 75.29032 135.3244 10181.31 120.5502 146.9158 17633.84 33.75448 119.3692
    pctMphr mbp  dpmaxdo  dobdose      age   baseEF    dobEF
1: 78.56989 156 18549.88 30.24194 67.34409 55.60394 65.24194

# Print frequency tables of all categorical variables with > 2 levels
cmult <- function(x) ! is.numeric(x) && length(unique(x)) > 2
tab <- function(x) {
  z <- table(x, useNA='ifany')
  paste(paste0(names(z), ': ', z), collapse=', ')
}
d[, lapply(.SD, tab), .SDcols=cmult]

                                      hxofCig
1: heavy: 122, moderate: 138, non-smoker: 298
                                   ecg
1: normal: 311, equivocal: 176, MI: 71

Tabulate all variables having between 3 and 10 distinct values and create a side effect when data.table is running that makes the summarization function tab store all values and frequencies in a growing list Z so that kable can render a markdown table after we pad columns to the maximum length of all columns (maximum number of distinct values).

# Using <<- makes data.table have a side effect of augmenting Z and
# Align in the global environment
tab <- function(x) {
  z <- table(x, useNA='ifany')
  i <- length(Z)
  Z[[i+1]] <<- names(z)
  Z[[i+2]] <<- as.vector(z)
  Align <<- c(Align, if(is.numeric(x)) 'r' else 'l', 'r')
  length(z)
}
discr <- function(x) { i <- length(unique(x)); i > 2 & i < 11 }
Z    <- list(); Align <- character(0)
w    <- d[, lapply(.SD, tab), .SDcols=discr]
maxl <- max(w)
# Pad shorter vectors with blanks
Z <- lapply(Z, function(x) c(x, rep('', maxl - length(x))))
Z <- do.call('cbind', Z)  # combine all into columns of a matrix
colnames(Z) <- rep(names(w), each=2)
colnames(Z)[seq(2, ncol(Z), by=2)] <- 'Freq'
knitr::kable(Z, align=Align)

dose	Freq	dobdose	Freq	hxofCig	Freq	ecg	Freq
10	2	5	7	heavy	122	normal	311
15	28	10	7	moderate	138	equivocal	176
20	47	15	55	non-smoker	298	MI	71
25	56	20	73
30	64	25	71
35	61	30	78
40	300	35	62
		40	205

A better approach is to let the kables function put together a series of separate markdown tables of different sizes. By using the “updating Z in the global environment” side effect we are able to let data.table output any type of objects of non-conformable dimensions over variables (such as frequency tabulations).

tab <- function(x) {
  z <- table(x, useNA='ifany')
  i <- length(Z)
  w <- matrix(cbind(names(z), z), ncol=2,
              dimnames=list(NULL, c(vnames[i+1], 'Freq')))
  Z[[i+1]] <<- knitr::kable(w, align=c(if(is.numeric(x)) 'r' else 'l', 'r'))
  length(z)
}
discr <- function(x) { i <- length(unique(x)); i > 2 & i < 11 }
Z      <- list()
vnames <- names(d[, .SD, .SDcols=discr])
w      <- d[, lapply(.SD, tab), .SDcols=discr]
knitr::kables(Z)

dose	Freq
10	2
15	28
20	47
25	56
30	64
35	61
40	300

dobdose	Freq
5	7
10	7
15	55
20	73
25	71
30	78
35	62
40	205

hxofCig	Freq
heavy	122
moderate	138
non-smoker	298

ecg	Freq
normal	311
equivocal	176
MI	71

Use a similar side-effect approach to get separate html describe output by gender.

g <- function(x, by) {
  Z[[length(Z) + 1]] <<- describe(x, descript=paste('age for', by))
  by
}
Z <- list()
by <- d[, g(age, gender), by=gender]
# Make Z look like describe() output for multiple variables
class(Z) <- 'describe'
attr(Z, 'dimensions') <- c(nrow(d), nrow(by))
attr(Z, 'descript') <- 'Age by Gender'
html(Z)

Age by Gender

2 Variables 558 Observations

age for male: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
220	0	51	0.999	67.86	12.91	45.95	51.00	62.00	69.00	75.00	81.00	86.00

lowest : 30 34 38 40 43 , highest: 88 89 91 92 93

age for female: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
338	0	58	0.999	67.01	13.74	47.00	50.70	59.25	68.00	76.00	83.00	85.00

lowest : 26 28 29 33 34 , highest: 87 88 89 90 91

# Compute a 1-valued statistic on multiple variables, by cross-classification
# of two variables.  Do this on a subset.  .SDcols=a:b uses variables in order
# Use keyby instead of by to order output the usual way
d[age < 70, lapply(.SD, mean), keyby=.(gender, newMI), .SDcols=pkhr:dp]

   gender newMI     pkhr      sbp       dp
1:   male     0 122.0561 147.7664 17836.24
2:   male     1 115.6667 140.6667 16437.67
3: female     0 122.8492 150.5084 18509.03
4: female     1 123.5714 171.5714 21506.71

# Compute multiple statistics on one variable
# Note: .N is a special variable: count of obs for current group
d[, .(Max=max(bhr), Min=min(bhr), Mean=mean(bhr), N=.N), by=.(gender, newMI)]

   gender newMI Max Min     Mean   N
1:   male     0 127  42 74.15385 208
2:   male     1  89  59 71.25000  12
3: female     0 210  45 75.96894 322
4: female     1 108  65 79.43750  16

# Same result another way
g <- function(x) list(Max=max(x), Min=min(x), Mean=mean(x), N=length(x))
d[, g(bhr), by=.(gender, newMI)]  # if g returned a vector instead, use as.list(g(bhr))

   gender newMI Max Min     Mean   N
1:   male     0 127  42 74.15385 208
2:   male     1  89  59 71.25000  12
3: female     0 210  45 75.96894 322
4: female     1 108  65 79.43750  16

d[, as.list(quantile(bhr)), by=gender]

   gender 0% 25% 50% 75% 100%
1:   male 42  63  72  83  127
2: female 45  65  75  85  210

# Compute multiple statistics on multiple variables
d[, lapply(.SD, quantile), by=gender, .SDcols=.q(bhr, pkhr, sbp)]

    gender bhr   pkhr    sbp
 1:   male  42  52.00  80.00
 2:   male  63 106.75 120.00
 3:   male  72 123.00 140.00
 4:   male  83 136.00 166.00
 5:   male 127 176.00 250.00
 6: female  45  61.00  40.00
 7: female  65 106.25 122.25
 8: female  75 122.00 141.50
 9: female  85 134.00 170.00
10: female 210 210.00 309.00

# Similar but put percentile number in front of statistic value
# Do only quartiles
g <- function(x) {
  z <- quantile(x, (1:3)/4, na.rm=TRUE)
  paste(format(names(z)), format(round(z)))
}
d[, lapply(.SD, g), by=gender, .SDcols=.q(bhr, pkhr, sbp)]

   gender    bhr    pkhr     sbp
1:   male 25% 63 25% 107 25% 120
2:   male 50% 72 50% 123 50% 140
3:   male 75% 83 75% 136 75% 166
4: female 25% 65 25% 106 25% 122
5: female 50% 75 50% 122 50% 142
6: female 75% 85 75% 134 75% 170

# To have more control over labeling and to have one row per sex:
g <- function(x) {
  s <- sapply(x, quantile, na.rm=TRUE)  # compute quantiles for all variables -> matrix
  h <- as.list(s)  # vectorizes first
  # Cross row names (percentile names) with column (variable) names
  # paste(b, a) puts variable name in front of percentile
  names(h) <- outer(rownames(s), colnames(s), function(a, b) paste(b, a))
  h
}
d[, g(.SD), by=gender, .SDcols=.q(bhr, pkhr, sbp)]

   gender bhr 0% bhr 25% bhr 50% bhr 75% bhr 100% pkhr 0% pkhr 25% pkhr 50%
1:   male     42      63      72      83      127      52   106.75      123
2: female     45      65      75      85      210      61   106.25      122
   pkhr 75% pkhr 100% sbp 0% sbp 25% sbp 50% sbp 75% sbp 100%
1:      136       176     80  120.00   140.0     166      250
2:      134       210     40  122.25   141.5     170      309

# Restrict to variables bhr - basedp in order columns created in data table
d[, g(.SD), by=gender, .SDcols=bhr : basedp]

   gender bhr 0% bhr 25% bhr 50% bhr 75% bhr 100% basebp 0% basebp 25%
1:   male     42      63      72      83      127        85     120.00
2: female     45      65      75      85      210        90     122.25
   basebp 50% basebp 75% basebp 100% basedp 0% basedp 25% basedp 50% basedp 75%
1:        130        145         203      5220    7976.25       9483   11183.50
2:        136        150         201      5000    8562.00      10063   11891.25
   basedp 100%
1:       16704
2:       27300

# Can put ! in front of a sequence of variables to do the opposite

# To add duplicated means to raw data use e.g.
# d[, Mean := mean(x), by=sex]

Merging Data

Consider a baseline dataset b and a longitudinal dataset L, with subject ID of id.

For more information see this, this, this, this and this. To merge any number of datasets at once and obtain a printed report of how the merge went, use the Hmisc Merge function.

b <- data.table(id=1:4, age=c(21, 28, 32, 23), key='id')
L <- data.table(id  = c(2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5),
                day = c(1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 2, 3),
                y    =  1 : 12, key='id')
b

    id day  y
 1:  2   1  1
 2:  2   2  2
 3:  2   3  3
 4:  3   1  4
 5:  3   2  5
 6:  3   3  6
 7:  3   4  7
 8:  4   1  8
 9:  4   2  9
10:  5   1 10
11:  5   2 11
12:  5   3 12

# Merge b and L to look up baseline age and associate it with all follow-ups
b[L, on=.(id)]   # Keeps all ids in L (left inner join)

    id age day  y
 1:  2  28   1  1
 2:  2  28   2  2
 3:  2  28   3  3
 4:  3  32   1  4
 5:  3  32   2  5
 6:  3  32   3  6
 7:  3  32   4  7
 8:  4  23   1  8
 9:  4  23   2  9
10:  5  NA   1 10
11:  5  NA   2 11
12:  5  NA   3 12

L[b, on=.(id)]   # Keeps all ids in b (right inner join)

    id day  y age
 1:  1  NA NA  21
 2:  2   1  1  28
 3:  2   2  2  28
 4:  2   3  3  28
 5:  3   1  4  32
 6:  3   2  5  32
 7:  3   3  6  32
 8:  3   4  7  32
 9:  4   1  8  23
10:  4   2  9  23

L[b, on=.(id), nomatch=NULL]  # Keeps only ids in both b and L (right outer join)

   id day y age
1:  2   1 1  28
2:  2   2 2  28
3:  2   3 3  28
4:  3   1 4  32
5:  3   2 5  32
6:  3   3 6  32
7:  3   4 7  32
8:  4   1 8  23
9:  4   2 9  23

uid <- unique(c(b[, id], L[, id]))
L[b[.(uid), on=.(id)]]         # Keeps ids in either b or c (full outer join)

    id day  y age
 1:  1  NA NA  21
 2:  2   1  1  28
 3:  2   2  2  28
 4:  2   3  3  28
 5:  3   1  4  32
 6:  3   2  5  32
 7:  3   3  6  32
 8:  3   4  7  32
 9:  4   1  8  23
10:  4   2  9  23
11:  5   1 10  NA
12:  5   2 11  NA
13:  5   3 12  NA

merge(b, L, by='id', all=TRUE) # also full outer join; calls merge.data.table

    id age day  y
 1:  1  21  NA NA
 2:  2  28   1  1
 3:  2  28   2  2
 4:  2  28   3  3
 5:  3  32   1  4
 6:  3  32   2  5
 7:  3  32   3  6
 8:  3  32   4  7
 9:  4  23   1  8
10:  4  23   2  9
11:  5  NA   1 10
12:  5  NA   2 11
13:  5  NA   3 12

For very large data tables, giving the data tables keys will speed execution, e.g.:

setkey(d, id)
setkey(d, state, city)

Join/merge can be used for data lookups:

s <- data.table(st=.q(AL, AK, AZ, CA, OK), y=5:1)
stateAbbrevs <- data.table(state=state.abb, State=state.name)
s[stateAbbrevs, , on=.(st=state), nomatch=NULL]

   st y      State
1: AL 5    Alabama
2: AK 4     Alaska
3: AZ 3    Arizona
4: CA 2 California
5: OK 1   Oklahoma

Reshaping Data

To reshape data from long to wide format, take the L data table above as an example.

w <- dcast(L, id ~ day, value.var='y')
w

   id  1  2  3  4
1:  2  1  2  3 NA
2:  3  4  5  6  7
3:  4  8  9 NA NA
4:  5 10 11 12 NA

# Now reverse the procedure
m <- melt(w, id.vars='id', variable.name='day', value.name='y')
m

    id day  y
 1:  2   1  1
 2:  3   1  4
 3:  4   1  8
 4:  5   1 10
 5:  2   2  2
 6:  3   2  5
 7:  4   2  9
 8:  5   2 11
 9:  2   3  3
10:  3   3  6
11:  4   3 NA
12:  5   3 12
13:  2   4 NA
14:  3   4  7
15:  4   4 NA
16:  5   4 NA

setkey(m, id, day)   # sorts
m[! is.na(y)]

    id day  y
 1:  2   1  1
 2:  2   2  2
 3:  2   3  3
 4:  3   1  4
 5:  3   2  5
 6:  3   3  6
 7:  3   4  7
 8:  4   1  8
 9:  4   2  9
10:  5   1 10
11:  5   2 11
12:  5   3 12

Analysis

Formatting

For analysis the sky is the limit. I take advantage of special formatting for model fit objects from the rms package by using html or latex methods and putting results='asis' in the chunk header to preserve the special formatting. Here is an example.

require(rms)
options(prType='html')  # needed to use special formatting (can use prType='latex')
set.seed(1)
n <- 1000
w <- data.table(x=runif(n), x2=rnorm(n), y=sample(0:1, n, replace=TRUE))
dd <- datadist(w); options(datadist='dd')  # rms needs for summaries and plotting
f <- lrm(y ~ x + rcs(x2, 4), data=w)
f

Logistic Regression Model

 lrm(formula = y ~ x + rcs(x2, 4), data = w)

	Model Likelihood Ratio Test	Discrimination Indexes	Rank Discrim. Indexes
Obs 1000	LR χ² 1.91	R² 0.003	C 0.526
0 492	d.f. 4	R²_4,1000 0.000	D_xy 0.051
1 508	Pr(>χ²) 0.7516	R²_4,749.8 0.000	γ 0.051
max \|∂log L/∂β\| 2×10^-14		Brier 0.249	τ_a 0.026

	β	S.E.	Wald Z	Pr(>\|Z\|)
Intercept	0.1079	0.2976	0.36	0.7169
x	0.1506	0.2197	0.69	0.4931
x2	0.0502	0.2142	0.23	0.8147
x2’	-0.3705	0.6631	-0.56	0.5763
x2’’	1.3624	2.6219	0.52	0.6033

anova(f)

	χ²	d.f.	P
Wald Statistics for `y`
x	0.47	1	0.4931
x2	1.44	3	0.6961
Nonlinear	0.33	2	0.8499
TOTAL	1.91	4	0.7523

Caching

The workhorse behind Rmarkdown and Quarto is knitr, which processes the code chunks and properly mingles code and tabular and graphical output. knitr has a built-in caching mechanism to make it so that code is not needlessly executed when the code inputs have not changed. This easy-to-use process does have two disadvantages: the dependencies are not transparent, and the stored cache files may be quite large. I like to take control of caching. To that end, the runifChanged function was written. Here is an example of its use. First a function with no arguments must be composed. This is the (usually slow) function that will be conditionally run if any of a group of listed objects has changed since the last time it was run. This function when needed to be run produces an object that is stored in binary form in a user-specified file (the default file name is the name of the current R code chunk with .rds appended).

# Read the source code for the hashCheck and runifChanged functions from
# https://github.com/harrelfe/rscripts/blob/master/hashCheck.r
getRs('hashCheck.r', put='source')
g <- function() {
  # Fit a logistic regression model and bootstrap it 500 times, saving
  # the matrix of bootstrapped coefficients
  f <- lrm(y ~ x1 + x2, x=TRUE, y=TRUE, data=dat)
  bootcov(f, B=500)
}
set.seed(3)
n   <- 2000
dat <- data.table(x1=runif(n), x2=runif(n),
                  y=sample(0:1, n, replace=TRUE))
# runifChanged will write runifch.rds if needed (chunk name.rds)
# Will run if dat or source code for lrm or bootcov change
b <- runifChanged(g, dat, lrm, bootcov)
dim(b$boot.Coef)

[1] 500   3

head(b$boot.Coef)

       Intercept          x1          x2
[1,]  0.02007292 -0.30079958  0.32416398
[2,]  0.06150624 -0.35741054  0.25522669
[3,]  0.25225861 -0.40094541  0.09290729
[4,]  0.13766665 -0.48661991  0.19684403
[5,] -0.22018456  0.02132711  0.33973578
[6,]  0.18217417 -0.36140896 -0.04873320

Parallel Computing

The runParallel function makes it easy to use available multiprocessor cores to speed up parallel computations especially for simulations. By default it runs the number of available cores, less one. runParallel makes the parallel package easier to use and does recombinations over per-core batches. The user writes a function that does the work on one core, and the same function is run on all cores. This function has set arguments and must return a named list. A base random number seed is given, and the seed is set to this plus i for core number i. The total number of repetitions is given, and this most balanced possible number of repetitions is run on each core to sum to the total desired number of iterations. runifChanged is again used, to avoid running the simulations if no inputs have changed.

# Load runParallel function from github
getRs('runParallel.r', put='source')

# Function to do simulations on one core
run1 <- function(reps, showprogress, core) {
  cof <- matrix(NA, nrow=reps, ncol=3,
                dimnames=list(NULL, c('a', 'b1', 'b2')))
  for(i in 1 : reps) {
    y <- sample(0:1, n, replace=TRUE)
    f <- lrm(y ~ X)
    cof[i, ] <- coef(f)
  }
  list(coef=cof)
}
# Debug one core run, with only 3 iterations
n    <- 300
seed <- 3
set.seed(seed)
X    <- cbind(x1=runif(n), x2=runif(n))  # condition on covariates
run1(3)

$coef
              a         b1        b2
[1,] -0.5455330  0.9572896 0.2215974
[2,] -0.2459193  0.3081405 0.1284809
[3,] -0.1391344 -0.2668562 0.1792319

nsim <- 5000
g <- function() runParallel(run1, reps=nsim, seed=seed)
Coefs <- runifChanged(g, X, run1, nsim, seed)
dim(Coefs)

[1] 5000    3

apply(Coefs, 2, mean)

            a            b1            b2 
 0.0020121803 -0.0007277216 -0.0003258610

Computing Environment

The following output is created by the command markupSpecs$html$session(), where markupSpecs is defined in the Hmisc package.

 R version 4.2.0 (2022-04-22)
 Platform: x86_64-pc-linux-gnu (64-bit)
 Running under: Pop!_OS 21.10
 
 Matrix products: default
 BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
 LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
 
 attached base packages:
 [1] stats     graphics  grDevices utils     datasets  methods   base     
 
 other attached packages:
 [1] rms_6.3-1         SparseM_1.81      data.table_1.13.6 Hmisc_4.7-0      
 [5] ggplot2_3.3.3     Formula_1.2-4     survival_3.2-13   lattice_0.20-45

To cite R in publications use:

R Core Team (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

To cite the Hmisc package in publications use:

Harrell Jr F (2022). Hmisc: Harrell Miscellaneous. R package version 4.7-0, https://hbiostat.org/R/Hmisc/.

To cite the rms package in publications use:

Harrell Jr FE (2022). rms: Regression Modeling Strategies. https://hbiostat.org/R/rms/, https://github.com/harrelfe/rms.

To cite the data.table package in publications use:

Dowle M, Srinivasan A (2020). data.table: Extension of 'data.frame'. R package version 1.13.6, https://CRAN.R-project.org/package=data.table.

To cite the ggplot2 package in publications use:

Wickham H (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. ISBN 978-3-319-24277-4, https://ggplot2.tidyverse.org.

To cite the survival package in publications use:

Therneau T (2021). A Package for Survival Analysis in R. R package version 3.2-13, https://CRAN.R-project.org/package=survival.